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Nathan Robinson

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AAAI Conference 2014 Conference Paper

Cost-Based Query Optimization via AI Planning

Nathan Robinson
Sheila McIlraith
David Toman

In this paper we revisit the problem of generating query plans using AI automated planning with a view to leveraging significant advances in state-of-the-art planning techniques. Our efforts focus on the specific problem of cost-based joinorder optimization for conjunctive relational queries, a critical component of production-quality query optimizers. We characterize the general query-planning problem as a deletefree planning problem, and query plan optimization as a context-sensitive cost-optimal planning problem. We propose algorithms that generate high-quality query plans, guaranteeing optimality under certain conditions. Our approach is general, supporting the use of a broad suite of domainindependent and domain-specific optimization criteria. Experimental results demonstrate the effectiveness of AI planning techniques for query plan generation and optimization.

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ICAPS Conference 2009 Conference Paper

SAT-Based Parallel Planning Using a Split Representation of Actions

Nathan Robinson
Charles Gretton
Duc Nghia Pham
Abdul Sattar 0001

Planning based on propositional SAT(isfiability) is a powerful approach to computing step-optimal plans given a parallel execution semantics. In this setting: (i) a solution plan must be minimal in the number of plan steps required, and (ii) non-conflicting actions can be executed instantaneously in parallel at a plan step. Underlying SAT-based approaches is the invocation of a decision procedure on a SAT encoding of a bounded version of the problem. A fundamental limitation of existing approaches is the size of these encodings. This problem stems from the use of a direct representation of actions — i. e. each action has a corresponding variable in the encoding. A longtime goal in planning has been to mitigate this limitation by developing a more compact split — also termed lifted — representation of actions in SAT encodings of parallel step-optimal problems. This paper describes such a representation. In particular, each action and each parallel execution of actions is represented uniquely as a conjunct of variables. Here, each variable is derived from action pre and post-conditions. Because multiple actions share conditions, our encoding of the planning constraints is factored and relatively compact. We find experimentally that our encoding yields a much more efficient and scalable planning procedure over the state-of-the-art in a large set of planning benchmarks.

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ICAPS Conference 2008 Conference Paper

A Compact and Efficient SAT Encoding for Planning

Nathan Robinson
Charles Gretton
Duc Nghia Pham
Abdul Sattar 0001

In the planning-as-SAT paradigm there have been numerous recent developments towards improving the speed and scalability of planning at the cost of finding a step-optimal parallel plan. These developments have been towards: (1) Query strategies that efficiently yield approximately optimal plans, and (2) Having a SAT procedure compute plans from relaxed encodings of the corresponding decision problems in such a way that conflicts in a plan arising from the relaxation are resolved cheaply during a post-processing phase. In this paper we examine a third direction of tightening constraints in order to achieve a more compact, efficient, and scalable SAT-based encoding of the planning problem. For the first time, we use lifting (i. e., splitting) and factoring to encode the corresponding n-step decision problems with a parallel action semantics. To ensure compactness we exploit reachability and neededness analysis of the plangraph. Our encoding also captures state-dependent mutex constraints computed during that analysis. Because we adopt a lifted action representation, our encoding cannot generally support full action parallelism. Thus, our approach could be termed approximate, planning for a number of steps between that required in the optimal parallel case and the optimal linear case. We perform a detailed experimental analysis of our approach with 3 state-of-the-art SAT-based planners using benchmarks from recent international planning competitions. We find that our approach dominates optimal SAT-based planners, and is more efficient than the relaxed planners for domains where the plan existence problem is hard.

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